Certified Compilation based on Gödel Numbers

2025-08-16

AI Summary

Compiler backdoor attacks undermine the trustworthiness of binaries by introducing deviations from their source code. Method: This paper proposes a Gödel-number–based certified compilation approach. Its core innovation is the first application of Gödel encoding to construct lightweight integer compilation certificates, enabling constant-time derivation rules that formally guarantee strict equivalence between source and binary in three dimensions: statement sets, execution order, and data dependencies. The method supports bidirectional certificate generation and machine-checked formal verification, establishing an end-to-end verifiable trusted compilation chain. Contribution/Results: We implement Charon, a prototype system compiling a subset of the FaCT language. Empirical evaluation confirms both theoretical soundness and engineering feasibility, significantly enhancing auditability and trust assurance throughout the compilation process.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Security and Privacy: Large-scale security measurements
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data

Abstract

In his 1984 Turing Award lecture, Ken Thompson showed that a compiler could be maliciously altered to insert backdoors into programs it compiles and perpetuate this behavior by modifying any compiler it subsequently builds. Thompson's hack has been reproduced in real-world systems for demonstration purposes. Several countermeasures have been proposed to defend against Thompson-style backdoors, including the well-known {it Diverse Double-Compiling} (DDC) technique, as well as methods like translation validation and CompCert-style compilation. However, these approaches ultimately circle back to the fundamental question: "How can we trust the compiler used to compile the tools we rely on?" In this paper, we introduce a novel approach to generating certificates to guarantee that a binary image faithfully represents the source code. These certificates ensure that the binary contains all and only the statements from the source code, preserves their order, and maintains equivalent def-use dependencies. The certificate is represented as an integer derivable from both the source code and the binary using a concise set of derivation rules, each applied in constant time. To demonstrate the practicality of our method, we present Charon, a compiler designed to handle a subset of C expressive enough to compile FaCT, the Flexible and Constant Time cryptographic programming language.

Problem

• Detect compiler backdoors in binary code representation
• Ensure binary matches source code integrity
• Generate certificates for trustworthy compiler outputs

Innovation

• Generates certificates for binary-source correspondence
• Uses integer-based certificate derivable from code
• Implements Charon compiler for C subset